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 :Choices:- 6 8 10 12
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 :Choices:- 6 8 10 12
Solution
Let's denote the sides of the triangle as follows:
PQ = x cm QR = y cm PR = z cm
From the problem, we have the following equations:
- y = 2x - 2 (since QR is less than twice the length of PQ by 2 cm)
- z = x + 10 (since PR exceeds the length of PQ by 10 cm)
- x + y + z = 40 (since the perimeter is 40 cm)
We can substitute equations 1 and 2 into equation 3 to solve for x:
x + (2x - 2) + (x + 10) = 40 4x + 8 = 40 4x = 32 x = 8
Substitute x = 8 into equations 1 and 2 to find y and z:
y = 2*8 - 2 = 14 z = 8 + 10 = 18
So, the lengths of the sides PQ, QR, and PR are 8 cm, 14 cm, and 18 cm respectively. Therefore, the smallest side of the triangle PQR is 8 cm.
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