The Galen Middle School is building a new bicycle storage shed in the school yard. On a carpenter's blueprint, the scale reads 1 in. = 3 ft. The frame for a doorway on the blueprint is shown as a in. Wide and 2a in. High. When the shed is built, what will be the actual dimensions of the doorway

Width = 3a

Height = 6a

Step-by-step explanation:

Given the following :

Scale = 1 in = 3 feets

Doorway frame on blueprint= a inches wide ; 2a inches High

Actual dimension of the doorway:

Since 1 in represent 3 feets

Actual doorway frame dimension will be :

Width = 3 * a = 3a

Height = 3 * 2a = 6a

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(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240