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Question
The width of a rectangle is 20 cm. the diagonal is 8 cm more than the length. Find the length of the rectangle.
20
23
22
21
ANSWER : 4
Descrption
<p style="margin-left:0px;">Let's denote the length of the rectangle as "L."</p><p style="margin-left:0px;">According to the given information, the width of the rectangle is 20 cm, and the diagonal is 8 cm more than the length, which can be expressed as:</p><p style="margin-left:0px;">Diagonal = L + 8</p><p style="margin-left:0px;">Now, we can use the Pythagorean Theorem to relate the length, width, and diagonal of the rectangle:</p><p style="margin-left:0px;">Diagonal^2 = Length^2 + Width^2</p><p style="margin-left:0px;">Plugging in the values we have:</p><p style="margin-left:0px;">(L + 8)^2 = L^2 + 20^2</p><p style="margin-left:0px;">Expanding and simplifying:</p><p style="margin-left:0px;">L^2 + 16L + 64 = L^2 + 400</p><p style="margin-left:0px;">Now, let's solve for L:</p><p style="margin-left:0px;">16L + 64 = 400</p><p style="margin-left:0px;">Subtract 64 from both sides:</p><p style="margin-left:0px;">16L = 400 - 64 16L = 336</p><p style="margin-left:0px;">Now, divide by 16:</p><p style="margin-left:0px;">L = 336 / 16 L = 21</p><p style="margin-left:0px;">So, the length of the rectangle is 21 cm.</p>
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