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Question
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. the length of the smallest side of the triangle PQR is:
6 cm
8 cm
9 cm
10 cm
ANSWER : 2
Descrption
<p style="margin-left:0px;">Let's denote the lengths of the sides of triangle PQR as follows:</p><p style="margin-left:0px;">PQ = x cm QR = (2x - 2) cm (QR is less than twice PQ by 2 cm) PR = (x + 10) cm (PR exceeds PQ by 10 cm)</p><p style="margin-left:0px;">Given that the perimeter of the triangle is 40 cm, we can write the equation:</p><p style="margin-left:0px;">PQ + QR + PR = 40</p><p style="margin-left:0px;">Substitute the expressions for PQ, QR, and PR:</p><p style="margin-left:0px;">x + (2x - 2) + (x + 10) = 40</p><p style="margin-left:0px;">Now, combine like terms:</p><p style="margin-left:0px;">4x + 8 = 40</p><p style="margin-left:0px;">Subtract 8 from both sides:</p><p style="margin-left:0px;">4x = 32</p><p style="margin-left:0px;">Now, divide by 4 to solve for x:</p><p style="margin-left:0px;">x = 32 / 4 x = 8</p><p style="margin-left:0px;">So, the length of the smallest side of triangle PQR, which is PQ, is 8 cm. The correct answer is 8 cm.</p>
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