<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770801443737-mxzzan9k6s.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzA4MDE0NDM3MzctbXh6emFuOWs2cy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzk0MzUxMDMxLCJleHAiOjE3OTQzNTEzMzF9.cTc373S1GaG7fZVfPclmdWc33ltsT8k4ihuOiYa6p40" style="max-width: min(150px, 100%); height: auto; display: block;" alt="The diagram shows a rectangle \(ABCD\) with side \(AB = (2\sqrt{2} + \sqrt{3})\) cm." class="aligncenter custom-width" /></figure></div>
<p>The diagram shows a rectangle \(ABCD\) in which \(AB = (2\sqrt{2} + \sqrt{3})\) cm. Given that the area of the rectangle is \((9 + \sqrt{6})\) cm\(^2\), find, without using a calculator,</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the exact value of \(BC\) in the form \((\sqrt{a} - \sqrt{b})\) cm, where&nbsp;\(a\) and \(b\) are integers.</span><span class="inline-marks">[4]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the exact value of \((AC)^2\) in the form \((c - \sqrt{d})\) cm\(^2\), where&nbsp;\(c\) and \(d\) are integers.</span><span class="inline-marks">[3]</span></div></li></ol>

The diagram shows a rectangle \(ABCD\) in which \(AB = (2\sqrt{2} + \sqrt{3})\) cm. Given that the area of the rectangle is \((9 + \sqrt{6})\) cm\(^2\), find, without using a calculator,

the exact value of \(BC\) in the form \((\sqrt{a} - \sqrt{b})\) cm, where \(a\) and \(b\) are integers.

the exact value of \((AC)^2\) in the form \((c - \sqrt{d})\) cm\(^2\), where \(c\) and \(d\) are integers.

IP3 Class Test (May 2025) Q3

IP3 Class Test (May 2025) Q3

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