Question

Given: KPST is a trapezoid, KP=ST, MN is a midsegment, MN=20, h=15, PS:KT=3:7 Find: KS and KP

Answer 1

KS=25, KP=17

Explanation:

Answer 2

The length of KS is 25 units and the length of KP is 17 units.

Explanation:

Given information: KPST is a trapezoid, KP=ST, MN is a mid segment, MN=20, h=15, PS:KT=3:7 .

Since two sides of the trapezoid are equal therefore it is an isosceles trapezoid.

The midsegment of a trapezoid is a line segment which connects the midpoints of the non-parallel sides.

The length of mid segment is average of length of parallel lines. The length of mid segment is 20.

It is given that PS:KT=3:7. Let the length of sides be 3x and 7x respectively.

`(3x+7x)/(2)=20`

`(10x)/(2)=20`

`5x=20`

`x=4`

The value of 3x and 7x are 12 and 28 respectively. So, the length of sides PS and KT is 12 and 28 respectively.

Use pythagoras in triangle AKP.

`AK^2+AP^2=KP^2`

`(8)^2+(15)^2=KP^2`

`√(64+225)=KP`

tex]\sqrt{289}=KP[/tex]

`17=KP`

Use pythagoras in triangle BKS.

`BK^2+BS^2=KS^2`

`(20)^2+(15)^2=KS^2`

`√(400+225)=KS`

tex]\sqrt{625}=KS[/tex]

`KS=25`

Therefore length of KS is 25 units and the length of KP is 17 units.