Triangle STV has sides ST = TV = 17, and SV = 16. What is the area?

Question

(A) 85
(B) 100
(C) 120
(D) 136
(E) 165

Kudos for a correct  solution .

Psiva00734 · Answer

ST=TV=17, SV=16.
Two sides area equal and third side is different 
it is ISOCELES TRIANGLE.
here two equal side, a=17, and b unequal side= 16
Area of triangle=b/4square root 4a2-b2
=16/4square root 4*17square-16square
=4*square root 1156-256
4*square root 900
=4*30=120
option C sufficient

Temurkhon · Answer

We have isoscele triangle where base=16 and two sides=17. To find area we should know height.

Property of isoscele triangles is that height=median.

So ,we have right triangle 17:8:height. Height=15 by 8:15:17 property

16*15/2=120

C

aj13783 · Answer

The fastest way to calculate is using the foll formula:

= Sq.rt.(S*(S-A)*(S-B)*(S-C))

Where S = (A+B+C)/2

A,B,C are the sides

S = (17+17+16)/2 = 50/2 = 25

Area = Sq.rt.(25*8*8*9)

= 5*8*3

= 120

Option C

iamdp · Answer

Hi
This is the Triangle ie an isosceles triangle

|\
| \17
| \
|h \
| 
| 
|_____ _\ 
<---8-----> 
Now according to Pythagorean theorem (17)^2=(H^2) + (8)^2 
From here we get h=15

Now area = 1/2* base * height = 1/2*16*15=120

KS15 · Answer

+1 for C. Area of Isosceles triangle= b/4 * Root of 4a^2-b^2
16/4 * Root of 4(17)^2- (16^2)
4* Root of 900
4*30=120

23a2012 · Answer

the answer is C
we need to find the hight lets call it TM where m is the middle of the basic SV
so we have MV= 8 and TV =17 
TM=Sq.rt 17^2-8^2 =15
so the area= 8*15 =120

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: Let’s think about this triangle: gpp_img11.png Triangle STV is isosceles, so the perpendicular line from vertex T is bisects base SV. Thus, SW = 8. Now, look at right triangle ATW: it has leg = 8 and hypotenuse = 17. It will save you a tremendous amount of calculations here if you already have memorized the 8-15-17 Pythagorean Triplet . Thus, TW = 15, and that’s the height. Area = (0.5)bh = (0.5)(16)(15) = 8*15 = 120. Answer = (C)

HouseStark · Answer

By using Heron's formula you can calculate the Area if you have given only sides of a Triangle.

A= \sqrt{s*(s-a)(s-b)(s-c)}

Here a,b,c is the sides of the triangle and s is the semi perimeter of the triangle

s=\frac{a+b+c}{2}

s=\frac{17+17+16}{2} = \frac{50}{2}=25

A= \sqrt{25*(25-17)(25-17)(25-16)}

A=120  (Answer)

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Triangle STV has sides ST = TV = 17, and SV = 16. What is the area?

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Triangle STV has sides ST = TV = 17, and SV = 16. What is the area?

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