Given:
The line passing through (-2,5) and (2,p) has a gradient of .
To find:
The value of p.
Solution:
If a line passes through two points, then the slope of the line is:
The line passing through (-2,5) and (2,p). So, the slope of the line is:
It is given that the gradient or slope of the line is .
On cross multiplication, we get
Divide both sides by 2.
Therefore, the value of p is 3.
The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.
<h3>Quadrilaterals</h3>There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.
<h3>System of Linear Equations</h3>System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
Perimeter=28cm
Area= 42 cm²
If the perimeter is the sum of all sides of the rectangle, you have:
Perimeter= 2b+2h=28
If the area of the rectangle is 42cm², you have:
Area=bh=42 cm²
You can write a system of linear equations.
2b+2h=28 (1)
bh=42 (2)
From equation 2, you have . Then, you can replace it in equation 1.
Now, you should solve the quadratic equation.
If h1=9.65 cm, then , and if h2=4.35 cm, then
.
Read more about the quadratic function here:
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