Construct A Right Triangle Whose Hypotenuse And One Side Measures 10 Cm And 8 Cm Respectively., Then Construct Another Triangle Whose Sides Are 4 /5 T

Construct a right triangle whose hypotenuse and one side measures 10 cm and 8 cm respectively.

Then construct another triangle whose sides are 4 /5 times the corresponding sides of this triangle

 

ANSWER:

Use the following information to draw the similar right triangles:

The hypotenuse and sides of the big right triangle are 10 cm,  8 cm and 6 cm, respectively.

The hypotenuse and corresponding sides of the small right triangle are 8 cm, 6.4 cm and 4.8 cm.

Step-by-step explanation:

Similar triangles have proportional sides.

The scale factor or ratio of small triangle to big triangle is 4/5 or 4:5.

The given measurements are sides of the big triangle because the small triangle is only 4/5 of the corresponding sides of the given right triangle:

Given measurements of big right triangle:

hypotenuse (the longest side of the right triangle): 10 cm

Side₁: 8 cm.

Find Side₂ using Pythagorean Theorem:

c² = a² + b²

Where c = hypotenuse, and  a and b = sides 1 and 2, respectively.

10² = 8² + b²

b² = 100 - 64

b = √(36)

b = 6  ⇒ Side₂ of the big triangle

Therefore, the hypotenuse and sides of the big right triangle are 10 cm,  8 cm and 6 cm, respectively.

Find the side of the small triangle which is 4/5 of the sides of the big right big triangle:

hypotenuse = (4/5)(10) = 8 cm

side₁ = (4/5)(8) = 32/5 or 6 ²/₅ cm  or  6.4 cm

side₂ = (4/5)(6) = 24/5  or  4 ⁴/₅ cm  or  4.8 cm.

Therefore, the hypotenuse and corresponding sides of the small right triangle are 8 cm, 6.4 cm and 4.8 cm.

Check:

Hypotenuse:

8:10 = 4:5

4:5 = 4:5  (True)

Side₁:

6.4 : 8 = 4:5

Multiple each value at the right side of equation by 10:

64 : 80 = 4:5

Divide each value at the right side by 16, its GCF:

4:5 = 4:5   (True)

Side₂:

4.8 : 6 = 4:5

Same procedure in checking as side 2:

48 : 60 = 4:5

4:5 = 4:5 (True)