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3 years ago

How do i solve this

Mathematics

1 answer:

sattari [20]3 years ago

8 0

Answer:

x = 13

Step-by-step explanation:

a right angle is 90 degrees and so you have to make both sides of that line add up to 90. so youre gonna want to add both sets of the numbers and equal it to 90 (90 = 53 + 24 + x) you can subtract 53 and 24 from both sides and youll be left with 13.

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DiKsa [7]

$\bold{\huge{\blue{\underline{ Solution }}}}$

<h3>Given :-</h3>

The right angled below is formed by 3 squares A, B and C
The area of square B has an area of 144 inches ²
The area of square C has an of 169 inches ²

We have to find the area of square A?

<h3>Let's Begin :- </h3>

The right angled triangle is formed by 3 squares

We have, 

Area of square B is 144 inches²
Area of square C is 169 inches²

We know that,

$\bold{ Area \: of \: square = Side × Side }$

Let the side of square B be x

Subsitute the required values,

$\sf{ 144 = x × x }$

$\sf{ 144 = x² }$

$\sf{ x = √144}$

$\bold{\red{ x = 12\: inches }}$

Thus, The dimension of square B is 12 inches

Area of square C = 169 inches

Let the side of square C be y

Subsitute the required values,

$\sf{ 169 = y × y }$

$\sf{ 169 = y² }$

$\sf{ y = √169}$

$\bold{\green{ y = 13\: inches }}$

Thus, The dimension of square C is 13 inches.

It is mentioned in the question that, the right angled triangle is formed by 3 squares

The dimensions of square be is x and y

Let the dimensions of square A be z

<h3>Therefore, By using Pythagoras theorem, </h3>

The sum of squares of base and perpendicular height equal to the square of hypotenuse

That is,

$\bold{\pink{ (Perpendicular)² + (Base)² = (Hypotenuse)² }}$

Here, 

Base = x = 12 inches
Perpendicular = z
Hypotenuse = y = 13 inches

Subsitute the required values,

$\sf{ (z)² + (x)² = (y)² }$

$\sf{ (z)² + (12)² = (169)² }$

$\sf{ (z)² + 144 = 169}$

$\sf{ (z)² = 169 - 144 }$

$\sf{ (z)² = 25}$

$\bold{\blue{ z = 5 }}$

Thus, The dimensions of square A is 5 inches

<h3>Therefore,</h3>

Area of square

$\sf{ = Side × Side }$

$\sf{ = 5 × 5 }$

$\bold{\orange{ = 25\: inches }}$

Hence, The area of square A is 25 inches.

6 0

2 years ago

How do i solve this​

How do i solve this