Question

Suppose the length of the base b of a rectangle is increased by 20 percent and the length of the altitude h is increased by 40 percent.

(a) Write an expression, in terms of b, that represents the length of the base of the rectangle after the 20% increase.

(b) Write an expression, in terms of h, that represents the length of the altitude of the rectangle after the 40% increase.

(c) Write an expression, in terms of b and h, that represents the area of the rectangle after both the lengths of the base and altitude are increased.

(d) Increasing a rectangle's base by 20% and altitude by 40% will increase the area by what percentage?

Answer 1

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Answer:

(a) 1.2b

(b) 1.4h

(c) A = 1.68bh

(d) 68%

Explanation:

(a) If 20% of b is added to b, you have ...

b + 0.20b = 1.2b

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(b) Similarly, if 40% of h is added to h, you have ...

1.4h

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(c) The area of the new rectangle is the product of the new dimensions:

A = (1.2b)(1.4h)

A = 1.68bh

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(d) The original rectangle area is A = bh, so the percentage change can be computed as ...

(A'/A -1)×100% = ((1.68bh)/(bh) -1)×100% = (1.68 -1)×100% = 68%

The given increases in base and height increase the area by 68%.