Answer:
b
Step-by-step explanation:
The sides of the triangle are 20 in, 48 in and 52 in
<u>Explanation:</u>
Given:
Let x be the length of smaller leg
Hypotenuse, H = x + 32
Height, h = x + 28
Length of the sides of a triangle = ?
If the triangle is a right angle triangle then we use pythagoras theorm to solve the question.
So,
(Hypotenuse)² = (height)² + (Base)²
(x + 32)² = (x + 28)² + (x)²
x² + 1024 + 64x = x² + 784 + 56x + x²
240 + 8x - x² = 0
x² - 8x - 240 = 0
Solving the quadratic equation:
x² + 12x - 20x - 240 = 0
x(x+12) - 20(x+12) = 0
(x-20) (x+12) = 0
(x-20) = 0
x = 20 in
Hypotenuse, H = x + 32
H = 20 + 32 in
H = 52 in
Height, h = x + 28
h = 20 + 28 in
h = 48 in
Therefore, the sides of the triangle are 20 in, 48 in and 52 in
20 : 5
Divide a common factor between these two numbers to simplify
Divide 5
20 / 5 = 4
5 / 5 = 1
The ratio simplified would be 4 : 1
Answer:
x = 6
Step-by-step explanation:
To find the missing side, write a proportion using side lengths from each similar shape. A proportion is an equation that sets equal two ratios.
Find x by cross multiplying numerator and denominator of each fraction.
4(18) = 12x
72 = 12x
6 = x