A, B & C form a triangle where BAC = 90° . AB = 7.3 mm and CA = 7.4 mm. Find the length of BC giving your answer rounded to 1 DP.

BC ≈ 10.4 mm(1 decimal)

Step-by-step explanation:

The question forms a right angle triangle. The angle BAC = 90°. The side AB = 7.3 mm and the side CA = 7.4 mm. The length of BC can be solved below.

AC = opposite side = 7.4 mm

AB = adjacent side = 7.3 mm

BC = hypotenuse = ?

Using pythagoras theorem we can find the longest side which is the hypotenuse

c² = a² + b²(pythagoras formular)

where

c = hypotenuse side

BC² = 7.4² + 7.3²

BC² = 54.76 + 53.29

BC² = 108.05

square root both sides

BC = √108.05

BC = 10.3947101931

BC ≈ 10.4 mm(1 decimal place)

the answer is 45 i just did it on oddesy ware

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240