MATHEMATICS MIDDLE SCHOOL

Complete the statement about the square pyramid shown below.x 5

Is x greater than 5 less than 5 or equal to 5?

Answers

Answer 1

Answer:

Answer:

x > 5

Step-by-step explanation:

We know:

If a, band care length of sides of a triangle, then

a + b > c

a + c > b

b + c > a

We have a = x, b = x, c = 10.

Substitute:

x + x > 10

2x > 10 divide both sides by 2

2x : 2 > 10 : 2

x > 5

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A square field had 3 m added to its length ad 2 m added to its width. The field then had an area of 90 m squared. Find the length of a side of the original field.

Answers

Answer:

The length of a side of the original field = 7 m.

Step-by-step explanation:

Here, the initial field is in form of a square.

Let us assume the side of the original square field = k meters

Now, the new length of the field = ( k + 3) m

The new width of the field = ( k + 2) m

So, the new field is now a rectangle with area = 90 sq. m

AREA OF A RECTANGLE = LENGTH x WIDTH

Here, the area of the new field = New length x new width

= ( k + 3) x ( k + 2)

$90 = ( k + 3) * ( k + 2)\n\implies k^2 + 2k + 3k + 6 = 90\nor, k^2 + 5 k - 84 = 0\n\implies k^2 + 12k - 7k -84 = 0\nor, k (k+12) -7(k+12) = 0\n\implies (k+12)(k-7) = 0$

⇒ either (k +12) = 0 ⇒ k = -12

or, ( k-7) = 0 ⇒ k = 7

But, here k = SIDE OF A FIELD, and it CANNOT be negative.

⇒ k = 7

Hence, the length of a side of the original field = 7 m.

Final answer:

To find the length of a side of the original field, you can solve the equation for the area of the expanded field.

Explanation:

To find the length of a side of the original field, we need to solve the equation for the area of the expanded field. Let's assume the original length of the square field is x meters. After adding 3 meters to its length and 2 meters to its width, the new length becomes (x+3) meters and the new width becomes (x+2) meters. The area of the expanded field is (x+3)(x+2) square meters, and it is given that this area is equal to 90 square meters. So, we have the equation (x+3)(x+2) = 90.

Next, we can solve this quadratic equation for x by factoring or using the quadratic formula. Once we find the value of x, we will have the length of a side of the original field.