Given: kpst is a trapezoid, kp=st, mn is a midsegment, mn=20, h=15, ps: kt=3: 7 find: ks and kp

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

Step-by-step 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.

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.

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

Use pythagoras in triangle BKS.

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

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

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