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Q.

If the area of a square is https://lh4.googleusercontent.com/ogp86330XmeEgQ22bWAqKf0YCJWIXRHnKiOIO7Dp08TlBn-lGe65W3lxstyDI_5i0vn4rsHEAMa1sAkqG1FoNS91QoyC3tV8-HGXHKnTz2m5eLQzJfxLdfPatYOjeciN5dUl6m-aNKo0c3b8UbEOTbA.Find the length of its diagonal.


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a

 https://lh5.googleusercontent.com/HuJYMKWo2pu3BW_MnxE-hU0aQG3WcI11giSaOKRXRkanDkN9F1CfOKoDTC-T1ugZaBGiXFz71RDUOPTkTrqfbg9lt2Do-u-zt6kzq1KhEGVaSITxzATP_mB6omG9bQLz3ojZo18qqeP0_rC-oLbwHWc

b

 https://lh6.googleusercontent.com/gAB_Uve1D4myaolRMJ2avBgmzwnQKLSLU2KESdwXXeGnfzTdRc1mygcWiQBCFwZWU0w5g6BZ0a1G485zj3j9p5ZKwA6cXcy_b9ehu8dq7ZfBvJ_aZ7gSdE_VWN370JNPdOOIPYel_meofC7BENklaQc

c

 https://lh3.googleusercontent.com/y__SDhf3FBLz8gIbPYN77nbv5R9jHO7eZFuuB6U5F6W-n05dTLOURhmBfdzx_LWWh9rgUMZyH_VdZaF2sNH6xxcsmfXuv0_2MHhaFvttyUPQI-Nf6l-VOurzMSIVq2aagDC_9VQpU9WdBALzVN9rnA4

d

 https://lh3.googleusercontent.com/Bb4zkl_IvSsnenTQCttPAP7mbgnDsXtA-GEzBlGs0O6p7lqiro_Sj18sZTazUqItiIb3RIuMkWsG2oARkF9AuuV_MNkkzWil5KvduJFDoH7_UaKFOIAlBMRpmZvMWnzT0R2minOQS5qe7WadjfhFDi4

answer is A.

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Detailed Solution

Concept:  We are given the area of the square and we have to find the length of its diagonal. Length of the side should be calculated first to know the value of the diagonal. Apply the formula, https://lh3.googleusercontent.com/yhUiUXS9TSfnkktVI-YCq2XWj-OW8g82cYmwkyAw0fFhMZU32mE65Ug1aQ07bwSKYA7p5yABqiNUhXUrmL_gOfYwzkonSXRZ5Mt0IKgZSC5mMytjUciHB0UwYZ95RNfyPNSk1_yCw-6cZN4g6GM9Vb4. Now for the diagonal put the value of side in this,  https://lh4.googleusercontent.com/vRoiNkKzrFP9s9sWbJZ6tv77lXog0P9WvjBi_pxD_QtfLobJWi4MWGwmP6EyhtQQ4RTXSPflAxkjkls46ZG1hUPGFmu4OZnWp34ZTuVgWfCUPs2MDfjeXx3E-VIo_8d5vd6SX5SCRsJQ_yj94fCnTzU.
Given that,
Area of the square is https://lh4.googleusercontent.com/ogp86330XmeEgQ22bWAqKf0YCJWIXRHnKiOIO7Dp08TlBn-lGe65W3lxstyDI_5i0vn4rsHEAMa1sAkqG1FoNS91QoyC3tV8-HGXHKnTz2m5eLQzJfxLdfPatYOjeciN5dUl6m-aNKo0c3b8UbEOTbAAs we know that,
https://lh3.googleusercontent.com/yhUiUXS9TSfnkktVI-YCq2XWj-OW8g82cYmwkyAw0fFhMZU32mE65Ug1aQ07bwSKYA7p5yABqiNUhXUrmL_gOfYwzkonSXRZ5Mt0IKgZSC5mMytjUciHB0UwYZ95RNfyPNSk1_yCw-6cZN4g6GM9Vb4It implies that, https://lh4.googleusercontent.com/CKTLipqiyTOiWAdZgrMI_Guzf7iMQCnWJYWQbdHlqAu-ipEG-e7o0g4-CY7PbTpjow5LcV5XLNwhJGnkNkWKuRSx_ByzCLtnHemkZywUSkKCvcLvVRH5sgYFrmrwWYE3na419KhGHAefdT-7JIZxeh8https://lh6.googleusercontent.com/NhYtXVlxOLeDz51bgVskCAWdmg-2kAwlBykdLduqwTZ52-PBqgTneDhejPvw4txebQPCgC4jmPMnHfXk2LZDH-4lefm0GKvZPTQrm651vKTwu7DogDIrozy3ezD9H840v96AaVbydF7UPYMJ26kWa2ASquare root both the sides of above equation,
https://lh4.googleusercontent.com/d_vlMWdJqqXbFLcvDaWmMb0RImYj0Ps8XZnhiGi7HtWzFmHn6dz6kqom6bZL3183LPZVIE8JzEwkIAHqQvIva0o-IKaC_e-kIJMMNlhim5Qf3uxIAYVr2_TNe-auNORUMstYWuIVi2cCbf1e5Sy_yU0https://lh4.googleusercontent.com/LWXyAnQWCPD5vqTDwn09MW8FCknoZoJGMEf6TFHP7OlFePWQcRbNlAPyCKbw_E_nHkg6FaOn-LBWa4WUnoSoqfEyxUEXP_qmIvC1vbeccx7KcgWXVXCCnbQb4J8aQ6xNwRqa2Y_ougtq_05oaYPgau0Now put https://lh3.googleusercontent.com/Ut2bl1xKaBfVgmNhD1dWwurIbuf7RgyKjVNvThG54Ae52A6ASnTI1o_HVG79DK8i2d1ywBf3qh36nFMEuZwbJCY47i1YJDGNFKFPZHIflPn2YVo_j6eCW0ZP5zzPenKCmg5kzrRq1rAYTadP3u1SFlA in https://lh4.googleusercontent.com/vRoiNkKzrFP9s9sWbJZ6tv77lXog0P9WvjBi_pxD_QtfLobJWi4MWGwmP6EyhtQQ4RTXSPflAxkjkls46ZG1hUPGFmu4OZnWp34ZTuVgWfCUPs2MDfjeXx3E-VIo_8d5vd6SX5SCRsJQ_yj94fCnTzUTherefore, https://lh3.googleusercontent.com/08DsomtzPGywKd4YEgJfL1yGytwUWBLzK_rIqOhkMKI0xmfjNywhjEQuoH3IsF52IkLhoJT918DIcFrppvbAOQSFx6xhsQryTdD2rhLjXlExdxDulkhO9DEBFnrL0xnxfBeBBG2j3uBdZlzWWsjDsVQHence, the correct answer is option 1) https://lh5.googleusercontent.com/HuJYMKWo2pu3BW_MnxE-hU0aQG3WcI11giSaOKRXRkanDkN9F1CfOKoDTC-T1ugZaBGiXFz71RDUOPTkTrqfbg9lt2Do-u-zt6kzq1KhEGVaSITxzATP_mB6omG9bQLz3ojZo18qqeP0_rC-oLbwHWc 
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