MATH SOLVE

4 months ago

Q:
# An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.A rectangle has a length of 6 inches and a width of 3 inches.What is the effect on the perimeter when the dimensions are multiplied by 8? The perimeter is increased by a factor of 8. The perimeter is increased by a factor of 24. The perimeter is increased by a factor of 64. The perimeter is increased by a factor of 256.This figure is made up of a triangle and a semicircle.What is the area of this figure?Use 3.14 for pi. Round only your final answer to the nearest tenth.Enter your answer, as a decimal, in the box.

Accepted Solution

A:

Q1.the given scale factor is 1:16

the area is 7 square feet

when calculating the area the scale factor is squared as well.

since the scale factor is 16, to find out area the scale should be squared that is,

16*16 = 256

then the new area is 7 square feet * 256

actual area = 256 * 7 = 1792 square feet

Q2. the rectangle with length 6 inches and width 3 inches.

the perimeter of the rectangle before changing dimensions are;

=(6*2) + (3*2)

= 12 + 6 = 18 inches

after multiplying the dimensions by 8,

new length = 6*8 = 48 inches

new width = 3*8 = 24 inches

new perimeter = (48*2) + (24*2)

= 96 + 48

= 144 inches

the perimeter ratio from new to old = 144:18

the perimeter has increased by (144/18) times

= 144/18 = 8

answer is perimeter increased by a factor of 8

q3)

area of the triangle

= 1/2 * height * base

= 1/2 * (5-2) *(4-(-3))

= 1/2 * 3 * 7

= 10.5 units²

area of semicircle

=pi*r2

r = 2-(-1.5)

= 3.5

area = 3.14 * (3.5)²

= 38.465 units²

total area = area of triangle + area of semicircle

= 10.5 + 38.465

= 48.965

round it off to the closest tenth

area = 49 units²

the area is 7 square feet

when calculating the area the scale factor is squared as well.

since the scale factor is 16, to find out area the scale should be squared that is,

16*16 = 256

then the new area is 7 square feet * 256

actual area = 256 * 7 = 1792 square feet

Q2. the rectangle with length 6 inches and width 3 inches.

the perimeter of the rectangle before changing dimensions are;

=(6*2) + (3*2)

= 12 + 6 = 18 inches

after multiplying the dimensions by 8,

new length = 6*8 = 48 inches

new width = 3*8 = 24 inches

new perimeter = (48*2) + (24*2)

= 96 + 48

= 144 inches

the perimeter ratio from new to old = 144:18

the perimeter has increased by (144/18) times

= 144/18 = 8

answer is perimeter increased by a factor of 8

q3)

area of the triangle

= 1/2 * height * base

= 1/2 * (5-2) *(4-(-3))

= 1/2 * 3 * 7

= 10.5 units²

area of semicircle

=pi*r2

r = 2-(-1.5)

= 3.5

area = 3.14 * (3.5)²

= 38.465 units²

total area = area of triangle + area of semicircle

= 10.5 + 38.465

= 48.965

round it off to the closest tenth

area = 49 units²