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

Length of KS and KP are; 25 and 17

Step-by-step explanation:

Given: KPST is a trapezoid, KP =ST, MN is a mid segment, h is the height =15

Also, MN = 20 , h = 15 and PS:KT = 3:7.

Since, the length of Mid-segment MN = 20.

Also, it is given: PS:KT = 3:7

Let bases PS = 3x and KT = 7x respectively.

then;

Simplify:

5x =20

Divide both sides by 5 we get;

x =4

Then:

Length of base PS = 3x = 3(4) = 12

and Length of base KT = 7x = 7(4) = 28.

In triangle PLK

Using Pythagoras theorem to find KP;

here, PL =h =15 and KL= 8 {you can see in the figure as shown below};

or

therefore, the length KP = 17

Construct a line: Join K and S

Now, in triangle KRS

KR = KL+LR = 8+12 = 20 and SR = h= 15

Using Pythagoras theorem in KRS to find KS ,

or

Therefore, the length of KS is, 25

468

step-by-step explanation:

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