Question

What is the length of SR?

9 units
12 units
15 units
18 units

Answer 1

Answer: The correct option is third, i.e.,15 units.

Explanation:

Given: Triangle QRS and STR are right angle triangles. RQ=20 and TQ=16.

Since angle SRT and angle RTQ are on a straight line, then these are complementary angle and the sum of these angles are 180 degree, therefore angle RTQ is 90 degree and the triangle RTQ isa right angle triangle.

Pythagoras formula,

$(perpendicular)^2+(base)^2=(hypotenuse)^2$

Using pythagoras in triangle RTQ, we get

$20^2=(RT)^2+16^2$

$(RT)^2=20^2-16^2\\(RT)^2=400-256\\(RT)^2=144\\(RT)=12$

Let length of SR be x.

Using pythagora in triangle STR we get,

$(ST)^2+12^2=x^2$

$(ST)^2=x^2-12^2\\ST=\sqrt{x^2-144}$

Using pythagora in triangle QRS we get,

$(SQ)^2=(RQ)^2+(SR)^2$

$(\sqrt{x^2-144}+16)^2=(20)^2+x^2$

$(\sqrt{x^2-144})^2+2(16)(\sqrt{x^2-144}))+(16)^2=400+x^2\\x^2-144+32\sqrt{x^2-144}+256=400+x^2\\\sqrt{x^2-144}=9\\x^2-144=81\\x^2=225\\x=15$

Therefore the length of SR is 15 units and third option is correct.

Answer 2

The length of SR as shown in the image is 15 units.

Similar figures

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

From the image, triangle SRT is similar to triangle TRQ. Since both triangles are right angles and they have one equal angle (∠T) as well as an equal side (RT)

Using Pythagoras:

RQ² = TQ² + TR²

20² = TR² + 16²

TR = 12

Hence:

SR/RQ = TR/TQ

SR / 20 = 12 / 16

SR = 15 units

The length of SR as shown in the image is 15 units.

Find out more on similar triangles at: https://brainly.com/question/2644832