Answer:
Part 1) The base is [tex]25\ in[/tex] and the height is [tex]10\ in[/tex]
Part 2) The base is [tex]7.5\ in[/tex] and the height is [tex]18.75\ in[/tex]
Step-by-step explanation:
case 1) Right isosceles triangle of the left
Let
x------> the base of the rectangle
y----> the height of the rectangle
Remember that
In a right isosceles triangle the lengths of the legs of the triangle is the same
[tex]y+x+y=45[/tex]
[tex]2y+x=45[/tex] ----> equation A
[tex]\frac{x}{y} =\frac{5}{2}[/tex]
[tex]x=2.5y[/tex] -----> equation B
substitute equation B in the equation A
[tex]2y+2.5y=45[/tex]
[tex]4.5y=45[/tex]
[tex]y=10\ in[/tex]
Find the value of x
[tex]x=2.5(10)=25\ in[/tex]
case 2) Right isosceles triangle of the right
Let
x------> the base of the rectangle
y----> the height of the rectangle
Remember that
In a right isosceles triangle the lengths of the legs of the triangle is the same
[tex]y+x+y=45[/tex]
[tex]2y+x=45[/tex] ----> equation A
[tex]\frac{y}{x} =\frac{5}{2}[/tex]
[tex]y=2.5x[/tex] -----> equation B
substitute equation B in the equation A
[tex]2(2.5x)+x=45[/tex]
[tex]6x=45[/tex]
[tex]x=7.5\ in[/tex]
Find the value of y
[tex]y=2.5(7.5)=18.75\ in[/tex]
