Mensuration part 7

Problem 1: The perimeter of an isosceles triangle is 32 cm and each of the equal sides is 5/6 times of the base. What is the area (in cm2) of the triangle?

Solution:

2a+b=32

2\times \frac{5}{6}b+b=32

\frac{10b+6b}{6}=32

b=12

2a=32-12=20

a=10

Area =\frac{b}{4}\sqrt{4\times 10^{2}-12^{2}}

\frac{12}{4}\times 16=48

Problem 2: Sides of a parallelogram are in the ratio 5 : 4. Its area is 1000 sq. units. Altitude on the greater side is 20 units. Altitude on the smaller side is?

Solution:

h_{1}\times b=h_{2}\times l

5x*20=4x*h

Height =25

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