Question

What is the perimeter of rectangle efgh? startroot 10 endroot startroot 29 endroot units 2 startroot 10 endroot 2 startroot 29 endroot units 22 units 39 units

Answer 1

The perimeter of the rectangle is the length of the boundary of the perimeter of the rectangle. The perimeter of the rectangle is 2(√29+√10).

What is the perimeter of the rectangle?

The perimeter of the rectangle is the length of the boundary of the perimeter of the rectangle.

In order to find the perimeter of the rectangle, we need to find the third side(Hypotenuse) of each triangle, therefore,

In ΔA,

$(Hypotenuse)^2 =(Perpendicular)^2+(Base)^2$

$GF^2 = 3^2+1^2\\GF=\sqrt{10}$

In ΔB,

$(Hypotenuse)^2 =(Perpendicular)^2+(Base)^2$

$EF^2 = 2^2+5^2\\EF=\sqrt{29}$

In ΔC,

$(Hypotenuse)^2 =(Perpendicular)^2+(Base)^2$

$GH^2 = 2^2+5^2\\GH=\sqrt{29}$

In ΔD,

$(Hypotenuse)^2 =(Perpendicular)^2+(Base)^2$

$EH^2 = 3^2+1^2\\EH=\sqrt{10}$

Now, the perimeter of the rectangle is,

$Perimeter\ EFGH = EF+ GF + GH +EH$

                              $=\sqrt{29}+\sqrt{10}+\sqrt{29}+\sqrt{10}\\\\=2\sqrt{29}+2\sqrt{10}\\\\=2(\sqrt{29}+\sqrt{10})$    

hence, the perimeter of the rectangle is 2(√29+√10).

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