The height of a triangle is 2 inches less than 4 times the l

The height of a triangle is 2 inches less than 4 times the length of its base. The area is 28 square inches. Find the length b of the base and the height h of the triangle. One positive integer is 8 less than 3 times another. Their product is 3. Find the integers. The area of the rectangular slab of foam insulation in the illustration is 4 square meters. Find the dimensions of the slab.

Solution

21 ) Given that

h = 4b - 2

Area of triangle = b x h = 28 square inches

b x (4b -2) = 28

4b²-2b-28 = 0

on solving,

b = 2.91 inches

h = 4 x 2.91 - 2

h = 9.64 inches

Therefore,

b = 2.91 inches,h = 9.64 inches

22 ) Given that

One positive integer is 8 less than 3 times another

let x,y are two positive integers

then

x = 3y -8

Given tat

Product of 2 integers = xy = 3

(3y -8)y= 3

3y²-8y-3 =0

On solving,

y = 3

then

x = 3 x 3 - 8 = 1

Hense,

Two integers are 1,3